{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Chapter 02: Single particle motion\n",
    "\n",
    "# *Isolated charge particles in electric and magnetic fields*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "This chapter deals with charge particle motion.\n",
    "\n",
    "Particles experience three different types of interactions\n",
    "1. collisions (direct or indirect): due to direct interaction between particles. \n",
    "1. grativity: when particles have mass\n",
    "1. electromagnetic forces: when particles have charge\n",
    "\n",
    "In this chapter, we ignore collisions. They will be treated in a different chapter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Force on a particle caused by gravity\n",
    "Gravitation is always present in any experiment in a laboratory or in astrophysical settings. However, it can be ignored when charged particles are surrounded by large electric fields or magnetic fields. However, one should always estimate the impact of any force to assess which are negligible and which is not. Ultimately, developing a model where all forces are taken into account will lead to unwanted complexity.\n",
    "\n",
    "Overall, the best approach is *back of the envelope* calculation before taking on big computational problems and apply the full force of numerical analysis to generate large 3-dimensional datasets. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Gravitational fields with small spatial variations\n",
    "When the change in gravitation is small compared to the particle trajectory, the force applied on a particle of mass $m$ is simply its weight. $$\\vec{F}=m\\vec{g}\\tag{2.1}$$\n",
    "We now need to define the trajectory as a function of time using Newton's second law $$\\frac{d\\vec{p}}{dt}=\\sum_i{\\vec{F_i}}$$\n",
    "$\\vec{p}$ is the particle momentum given by $\\vec{p}=m\\vec{v}$ using the particle mass and it velocity $\\vec{v}$. Clearly, we have only one force here! So, we shall simplify it right away to\n",
    "$$\n",
    "\\frac{d\\vec{p}}{dt}=m\\vec{g}\\tag{2.2}\n",
    "$$\n",
    "It is possible to integrate Eq. $(2.2)$ using a very simple integration method for Ordinary Differential Equations. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Integrating first order ordinary differential equations\n",
    "Newton's second law, i.e. Eq. $(2.1)$, can be discretized. Discretization means in this context that $dt$, representing an infinitely small amount of time, is turned into $\\Delta t$, a finite amount of time. We can rewrite Newton's law as\n",
    "$$\\frac{\\Delta p}{\\Delta t}=\\vec{F}\\tag{2.3}.$$\n",
    "Clearly, we get from this $p_{t+\\Delta t}-p_t=\\vec{F}\\Delta t$.  If we know the momentum and the force at $t$, then we can compute the new momentum at $\\Delta t$. To extract the trajectory from this equation, we have to realize that $\\vec{v}=\\frac{d\\vec{r}}{dt}$ where $\\vec{r}(t)=(x(t),y(t),z(t))$, the coordinate of the particle at the time $t$. We can rewrite Eq. $(2.3)$ as $$m\\vec{v}_{t+\\Delta t}-m\\vec{v}_t=m\\vec{g}\\Delta t$$ or $$\\vec{v}_{t+\\Delta t}-\\vec v_t=\\vec g\\Delta t$$\n",
    "It seems that **this trajectory does not dependent on the particle mass!** This is a remarkable result. An electron inside a gravitational field falls as fast as a proton, which is 2000 times more massive. We need to expand this equation to our coordinate system $(x,y,z)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Here is the system of equations we need to solve for.\n",
    "$$v_{x,t+\\Delta t}=g_x\\Delta t+v_{x,t}\\\\\n",
    "v_{y,t+\\Delta t}=g_y\\Delta t+v_{y,t}\\\\\n",
    "v_{z,t+\\Delta t}=g_z\\Delta t+v_{z,t}$$\n",
    "However, this system is not giving the trajectory $(x(t),y(t),z(t))$ but the velocity $(v_x(t),v_y(t),v_z(t))$. Fortunately, we know that $\\vec{v}=\\frac{d\\vec{r}}{dt}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now we find the trajectory using \n",
    "$$x_{t+\\Delta t}=v_{x,t+\\Delta t}\\Delta t+x_t\\\\\n",
    "y_{t+\\Delta t}=v_{y,t+\\Delta t}\\Delta t+y_t\\\\\n",
    "z_{t+\\Delta t}=v_{z,t+\\Delta t}\\Delta t+z_t$$\n",
    "We are now ready to do some computations using python. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Using python to solve the free fall of an electron inside Earth's gravity\n",
    "We are going to solve equation $(2.1)$ using the following conditions. First, $$\\vec{g}=(0,g_y,0)$$ with $g_y=-9.81m/s^2$. Our initial conditions are $$v_x=0\\\\v_y=0\\\\v_z=0$$ and $$x=0\\\\y=0\\\\z=0$$ Clearly, nothing happens in the z direction. So, we will ignore it for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's start by importing our tools into the python code, [math](https://docs.python.org/2/library/math.html), [numpy](http://www.numpy.org/) and [matplotlib](https://matplotlib.org/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import math\n",
    "from math import sqrt as sqrt\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#to display inside the notebook!\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Then we define our main (i.e. global) variables, all in mks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#initial time\n",
    "t_initial=0\n",
    "#final time \n",
    "t_final=10\n",
    "#time step\n",
    "dt=0.5 \n",
    "#number of time steps declared as integer\n",
    "n = int((t_final-t_initial)/dt) \n",
    "#electron mass\n",
    "m=9.10938356e-31 \n",
    "#gravity at sea level\n",
    "gx=0 \n",
    "gy=-9.81\n",
    "#initial velocity\n",
    "vx_initial=0\n",
    "vy_initial=0\n",
    "#we use the momemtum to be physically sound, even if using velocity is more computationally effecient\n",
    "px_initial=m*vx_initial\n",
    "py_initial=m*vy_initial\n",
    "#initial position\n",
    "x_initial=0 \n",
    "y_initial=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now we declare our arrays. While in python we do not have to declare variables like in C or Fortran, arrays are special. Here we just declare at one element using np (i.e. numpy). However, since we know the total number of steps, we could have assigned them right from the start. **Avoid using `np.empty(...)` as this function allocates memory but does not set it to a given value (like 0s).**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "x=np.zeros(1)\n",
    "y=np.zeros(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We now declare other variables which will be used inside the main part of the code. Technically we do not have to do this, but it makes the code more readable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "px_old=px_initial \n",
    "py_old=py_initial \n",
    "x_old=x_initial \n",
    "y_old=y_initial "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We now work on our main loop. It contains the algorithm that will solve our ordinary differential equation. We start with the `for` loop.\n",
    "```for i in range(1,n,1): ```\n",
    "This loop goes from `1` to `n` with a step of `1`. Note that there is a column `:` at the end that indicates to python that the code included in the loop is below. Indentations are used to tell python which piece of code is in the loop. So **indentations are important in python**. To put a piece of code outside of the loop, you need to indent back to the left."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(1,n,1): \n",
    "    fx=m*gx #this is the force along x\n",
    "    fy=m*gy #this is the force along y   \n",
    "    px_new=fx*dt+px_old #new momentum\n",
    "    py_new=fy*dt+py_old\n",
    "    vx=px_new/m #new velocity\n",
    "    vy=py_new/m\n",
    "    x_new=vx*dt+x_old #new position\n",
    "    y_new=vy*dt+y_old\n",
    "    x=np.append(x,[x_new]) #the positions are appended at the end of the x and y arrays.\n",
    "    y=np.append(y,[y_new])\n",
    "    x_old=x_new # we now replace the old data with the new ones\n",
    "    y_old=y_new\n",
    "    px_old=px_new\n",
    "    py_old=py_new\n",
    "# and the loop starts again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "`i` is the step counter going from `1` to `n`, with s step of `1`. Note the indent to indicate python that this piece of code is inside the `for` loop. Note that we note only compute the components of the force $\\vec{F}$ `fx` and `fy` but both variables are also declared at the same time. This goes for the other variables also. It is time to plot the results now"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n",
    "# Now, we draw our points with a gradient of colors.\n",
    "ax.scatter(x, y, c=range(n), linewidths=0,marker='o', s=15, cmap=plt.cm.jet,)\n",
    "ax.axis('equal')\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "So we have just plotted the electron trajectory inside the Earth gravitational field. Each dot corresponds to the position of the particle at each time steps, the time difference is constant. The increasing distance between each point is sign of acceleration. But we can also interpolate the whole trajectory by adding points in between. These points are used to make the graph more readable. However, since they are not computed with the main algorithm they are only an approximation of the trajectory. Let's create two other arrays that interpolates the initial arrays `x` and `y`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "k = 100\n",
    "x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, x)\n",
    "y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And see what we get"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(8, 8))\n",
    "# Now, we draw our points with a gradient of colors.\n",
    "ax.scatter(x_interpolated, y_interpolated, c=range(n*k), linewidths=0,\n",
    "           marker='o', s=15, cmap=plt.cm.jet,)\n",
    "ax.axis('equal')\n",
    "ax.set_axis_off()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can make a simple plotting function by rewriting the code above slightly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def plot_2D(x,y,n_interpolated,plot_size,plot_axes):\n",
    "    n = len(x)\n",
    "    k = n_interpolated\n",
    "    x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, x)\n",
    "    y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, y)\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(plot_size, plot_size))\n",
    "    # Now, we draw our points with a gradient of colors.\n",
    "    ax.scatter(x_interpolated, y_interpolated, c=range(n*k), linewidths=0,\n",
    "               marker='o', s=2*plot_size, cmap=plt.cm.jet,) #s is the size of the plotted symbol 'o'\n",
    "    ax.axis('equal')\n",
    "    if (plot_axes!=\"axes\"):#so we can switch the axis on or off\n",
    "        ax.set_axis_off()\n",
    "    else:\n",
    "        plt.xlabel(\"x (m)\")\n",
    "        plt.ylabel(\"y (m)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And we can print easily now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2D(x_interpolated,y_interpolated,10,4,\"no\")\n",
    "plot_2D(x_interpolated,y_interpolated,10,4,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Entr'acte\n",
    "Let's take a break from physics and see if we can use a function to integrate Eq. $(2.3)$.  We can reuse the `for` loop above to generate an ordinary differential equation integrator using $x_0$, $y_0$, $v_{x,0}$, $v_{y,0}$, $t_{initial}$, $t_{final}$ and the number of steps $n_{steps}$ as inputs. We define it as\n",
    "```python\n",
    "def OED_integration(x_initial,y_initial,vx_initial,vy_initial,t_initial,t_final,n_steps):\n",
    "```\n",
    "The other variables, like `m`, `t`, `dt`, ... are kept as is and do not have to be part of the input of OED_integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def ODE_integration(x_initial,y_initial,vx_initial,vy_initial,t_initial,t_final,n_steps):\n",
    "    x=np.full(1,x_initial) # we do this to initialize the x variable as a numpy array\n",
    "    y=np.full(1,y_initial)\n",
    "    px_old=vx_initial*m\n",
    "    py_old=vy_initial*m\n",
    "    dt=(t_final-t_initial)/n_steps\n",
    "    for i in range(1,n_steps,1): \n",
    "        fx=m*gx #this is the force along x\n",
    "        fy=m*gy #this is the force along y   \n",
    "        px_new=fx*dt+px_old #new momentum\n",
    "        py_new=fy*dt+py_old\n",
    "        vx=px_new/m #new velocity\n",
    "        vy=py_new/m\n",
    "        x_new=vx*dt+x[i-1] #new position\n",
    "        y_new=vy*dt+y[i-1] # in python arrays start at index 0\n",
    "        x=np.append(x,x_new) #the positions are appended at the end of the x and y arrays.\n",
    "        y=np.append(y,y_new)\n",
    "        \"\"\"The ones below are not needed. We use the ones from the previous step inside the array\n",
    "        x_old=x_new \n",
    "        y_old=y_new\"\"\"\n",
    "        px_old=px_new\n",
    "        py_old=py_new\n",
    "    return x,y\n",
    "# and the loop starts again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We then create two new arrays and fill them up using `ODE_integration(x_initial,y_initial,vx_initial,vy_initial,t_initial,t_final,n_steps)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y=ODE_integration(0,0,10,10,0,3,80)\n",
    "plot_2D(x,y,10,8,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Electrostatic force\n",
    "\n",
    "It is now time to move on to electrostatic forces. A particle with charge $q$ placed inside an electric field $\\vec{E}$ is submitted to a force \n",
    "$$\\vec F=q\\vec E\\tag{2.4}$$\n",
    "Does this formula remind you of another one seen before?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Physical model\n",
    "Indeed, the particle feels a force that looks like gravity (i.e. Eq. $2.1$). However, there is a subtle difference when we use Newton's second law\n",
    "$$ m\\frac{d\\vec v}{dt}=q\\vec E$$\n",
    "This time around the mass does not go away and we expect the trajectory to depend on the mass. Here is the new system of equations we need to solve for.\n",
    "$$v_{x,t+\\Delta t}=\\frac{q}{m}E_x\\Delta t+v_{x,t}\\\\\n",
    "v_{y,t+\\Delta t}=\\frac{q}{m}E_y\\Delta t+v_{y,t}\\\\\n",
    "v_{z,t+\\Delta t}=\\frac{q}{m}E_z\\Delta t+v_{z,t}$$\n",
    "And since $\\vec{v}=\\frac{d\\vec{r}}{dt}$ we get the same system as before for the coordinates, i.e.\n",
    "$$x_{t+\\Delta t}=v_{x,t+\\Delta t}\\Delta t+x_t\\\\\n",
    "y_{t+\\Delta t}=v_{y,t+\\Delta t}\\Delta t+y_t\\\\\n",
    "z_{t+\\Delta t}=v_{z,t+\\Delta t}\\Delta t+z_t$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Using python to solve the free fall of an electron inside an electric field\n",
    "We are going to solve equation $(2.1)$ using the following conditions. First, $$\\vec E=(0,E_y,0)$$ with $E_y=-1 V/m$. Our initial conditions are $$v_x=0\\\\v_y=0\\\\v_z=0$$ and $$x=0\\\\y=0\\\\z=0$$ Clearly, nothing happens in the z direction. So, we will ignore it for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's redefine our ODE integrator to cope with this new force. We need to initialize the charge of our electron and the electric field in which it is moving, all in MKS. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "q=-1.60217662e-19\n",
    "Ex=0\n",
    "Ey=1\n",
    "vx_final=0\n",
    "vy_final=0\n",
    "clight=299792458"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And then we make our new function, named `OED_integration_E`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def ODE_integration_E(x_initial,y_initial,vx_initial,vy_initial,t_initial,t_final,n_steps):\n",
    "    x=np.full(1,x_initial) # we do this to initialize the x variable as a numpy array\n",
    "    y=np.full(1,y_initial)\n",
    "    px_old=vx_initial*m\n",
    "    py_old=vy_initial*m\n",
    "    dt=(t_final-t_initial)/n_steps\n",
    "    for i in range(1,n_steps,1): \n",
    "        fx=q*Ex #this is the force along x\n",
    "        fy=q*Ey #this is the force along y   \n",
    "        px_new=fx*dt+px_old #new momentum\n",
    "        py_new=fy*dt+py_old\n",
    "        vx=px_new/m #new velocity\n",
    "        vy=py_new/m\n",
    "        x_new=vx*dt+x[i-1] #new position\n",
    "        y_new=vy*dt+y[i-1] # in python arrays start at index 0\n",
    "        x=np.append(x,x_new) #the positions are appended at the end of the x and y arrays using numpy.\n",
    "        y=np.append(y,y_new)\n",
    "        px_old=px_new\n",
    "        py_old=py_new\n",
    "    print(vx/clight,vy/clight)\n",
    "    print(x[n_steps-1],\"m\",y[n_steps-1],\"m\")\n",
    "    return x,y\n",
    "# and the loop starts again."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Can you guess what changed??"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Besides the name (which we changed to avoid overriding the previous function), we changed only two lines\n",
    "```\n",
    "fx=q*Ex #this is the force along x\n",
    "fy=q*Ey #this is the force along y   \n",
    "```\n",
    "We could do this because the previous code conversed physical information and separated force and momentum. While being less efficient computationally, we were able to reuse the code, mostly unchanged."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "So let's run it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 -1759.1576096745716\n",
      "0.0 m -791073275720.6312 m\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y=ODE_integration_E(0,0,0,0,0,3,2000)\n",
    "plot_2D(x,y,1,8,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "That's a long way down. And the velocity is enormous. Did we do something wrong? Let's check it by integrating analytically and make sure the code is correct!\n",
    "$$ \\frac{d^2y}{dt^2}=\\frac{q}{m}E_y\\\\\n",
    "\\frac{dy}{dt}=\\frac{q}{m}E_y t+v_{y0}=\\frac{q}{m}E_y t$$\n",
    "We integrate one last time to get the trajectory\n",
    "$$y=\\frac{q}{2m}E_y t^2+y_0=\\frac{q}{2m}E_y t^2\\tag{2.5}$$\n",
    "So, for an electron moving inside an electric field of $1V/m$ we get"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-791469010225.7589 m\n"
     ]
    }
   ],
   "source": [
    "print(q*Ey/(2.*m)*3.**2,\"m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Well! The code gives a very similar answer to the analytical solution. They are not exactly the same because the numerical integration can only be as exact as the analytical solution of Eq. $(2.5)$ for a number of steps that is infinitely large. Of course, we know that the special law of relatively need to be invoked to limit the speed of the electron below the speed of light. So we have integrated our ODE for too long, as the output velocities show. Let's do it for a shorter time, let's say $3\\mu s$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 -0.0016720357470644369\n",
      "0.0 m -0.7518955597144708 m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y=ODE_integration_E(0,0,0,0,0,3e-6,20)\n",
    "plot_2D(x,y,1,8,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Well we are now only at 0.16% the speed of light. So, we can accept that our solution is physically sound. Now let's see if we give an initial velocity of $200km/s$ in both direction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0006671281903963041 -0.002217377922960473\n",
      "0.9833333333333347 m -1.1785496112648044 m\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x,y=ODE_integration_E(0,0,2e5,2e5,0,5e-6,60)\n",
    "plot_2D(x,y,1,8,\"axes\")"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "While at our geometrical scale, the structure of the gravitational field is straightforward, electric field distributions can be more complex. For instance, the electric field generated by one single particle with charge q is given by $$\\vec{E}=\\frac{1}{4\\pi\\varepsilon_0}\\frac{q}{r^2}\\hat{r}\\tag{2.6}.$$ Here $r$ is the distance between the point where the field is measured and the particle location. $\\hat{r}$ is the unit vector direction, looking at the measurement location from the charge point of view.\n",
    "![image.png](attachment:image.png)\n",
    "**Figure 1: The geometry used to compute the electric field generated by a charge q at a remote location (the cross).**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "If the particle is located at $(x_p,y_p,z_p)$ and we measure the field at the position $(x,y,z)$ then $r$ is simply $$r=\\sqrt{(x-x_p)^2+(y-y_p)^2+(z-z_p)^2}$$ and $$\\hat{r}=\\frac{x-x_p}{r}\\hat{x}+\\frac{y-y_p}{r}\\hat{y}+\\frac{z-z_p}{r}\\hat{z}.$$\n",
    "We now take the previous electron and drop it in the electric field created by an immobile proton, with charge $q=+1.6\\times10^{-19}C$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def ODE_integration_E_with_charge(charge_location,charge_value,initial_position,initial_velocity,time_frame,n_steps):\n",
    "    loc=np.zeros((3,n_steps)) #index 0 is x, index 1 is y and index 2 is z \n",
    "    loc[:,0]=initial_position\n",
    "    \"\"\" Let's start to use vectors and combine notations\n",
    "    the column : is equivalent to writing\n",
    "    loc[0,0]=initial_position[0]\n",
    "    loc[1,0]=initial_position[1] \n",
    "    loc[2,0]=initial_position[2]\n",
    "    \"\"\"\n",
    "    v_old=initial_velocity\n",
    "    dt=(time_frame[1]-time_frame[0])/n_steps\n",
    "    E=[0,0,0]\n",
    "    f=np.zeros(3)\n",
    "    v_new=np.zeros(3)\n",
    "    for i in range(1,n_steps,1):\n",
    "        r=sqrt((loc[0,i-1]-charge_location[0])**2+(loc[1,i-1]-charge_location[1])**2+(loc[2,i-1]-charge_location[2])**2)\n",
    "        if (r<1e-7):\n",
    "            r=1e-7 # we won't divide by 0\n",
    "        r_unit=(loc[:,i-1]-charge_location)/r\n",
    "        E=1./(4*3.1416*8.85e-12)*charge_value/r**2*r_unit \n",
    "        f=q*E\n",
    "        v_new=f/m*dt+v_old #new velocity\n",
    "        loc[:,i]=v_new*dt+loc[:,i-1] #new position\n",
    "        v_old=v_new\n",
    "    return loc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now let's define a new plotting function that indicates where the motionless charge is located"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def plot_2D_with_charge(rc,x,y,n_interpolated,plot_size,plot_axes):\n",
    "    n = len(x)\n",
    "    k = n_interpolated\n",
    "    x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, x)\n",
    "    y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, y)\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(plot_size, plot_size))\n",
    "    # Now, we draw our points with a gradient of colors.\n",
    "    ax.scatter(x_interpolated, y_interpolated, c=range(n*k), linewidths=0,\n",
    "               marker='o', s=2*plot_size, cmap=plt.cm.jet,) #s is the size of the plotted symbol 'o'\n",
    "    ax.scatter(rc[0], rc[1], c='black', linewidths=0,\n",
    "               marker='x', s=3*plot_size,) \n",
    "    ax.axis('equal')\n",
    "    if (plot_axes!=\"axes\"):#so we can switch the axis on or off\n",
    "        ax.set_axis_off()\n",
    "    else:\n",
    "        plt.xlabel(\"x (m)\")\n",
    "        plt.ylabel(\"y (m)\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rc=[4e-3,0,0] #charge location\n",
    "qc=1.6e-19 #charge value\n",
    "loc=ODE_integration_E_with_charge(rc,qc,(-5e-3,10e-4,0),(500,0,0),(0,50e-6),1000)\n",
    "plot_2D_with_charge(rc,loc[0,:],loc[1,:],1,7,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Magnetic force\n",
    "\n",
    "After looking at electrostatic forces, we now study magnetic forces. A particle of charge $q$ and traveling at a velocity $\\vec v$ inside a magnetic field $\\vec{B}$ is given by $$\\vec F=q\\vec v\\times \\vec B$$ In this case, the equation of motion is given by $$m\\frac{d\\vec v}{dt}=q\\vec v\\times \\vec B\\tag{2.7}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Physical model\n",
    "We now have a more complex behavior since the system\n",
    "$$\\frac{dv_x}{dt}=\\frac{q}{m}(v_yB_z-v_zB_y)\\\\\n",
    "\\frac{dv_y}{dt}=\\frac{q}{m}(v_zB_x-v_xB_z)\\\\\n",
    "\\frac{dv_z}{dt}=\\frac{q}{m}(v_xB_y-v_yB_x)$$\n",
    "formed a set of coupled ODEs. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This can be resolved by deriving in time to obtain\n",
    "$$\\frac{d^2v_x}{dt^2}=\\frac{q}{m}(\\frac{dv_y}{dt}B_z-\\frac{dv_z}{dt}B_y)\\\\\n",
    "\\frac{d^2v_y}{dt^2}=\\frac{q}{m}(\\frac{dv_z}{dt}B_x-\\frac{dv_x}{dt}B_z)\\\\\n",
    "\\frac{dv_z}{dt}=\\frac{q}{m}(\\frac{dv_x}{dt}B_y-\\frac{dv_y}{dt}B_x)$$\n",
    "So we can include $v_x$ inside the equation that has $d^2v_x/dt^2$, ..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's suppose that we align the coordinate system along $\\vec{B}$ so that $\\vec{B}=B\\hat z$ we have\n",
    "$$\\frac{dv_x}{dt}=\\frac{q}{m}v_yB\\\\\n",
    "\\frac{dv_y}{dt}=-\\frac{q}{m}v_xB\\\\\n",
    "\\frac{dv_z}{dt}=0$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This can be resolved by deriving in time to obtain\n",
    "$$\\frac{d^2v_x}{dt^2}=\\frac{q}{m}\\frac{dv_y}{dt}B\\\\\n",
    "\\frac{d^2v_y}{dt^2}=-\\frac{q}{m}\\frac{dv_x}{dt}B\\\\\n",
    "\\frac{dv_z}{dt}=0$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "And we get \n",
    "$$\\frac{d^2v_x}{dt^2}+\\Big(\\frac{qB}{m}\\Big)^2v_x=0\\\\\n",
    "\\frac{d^2v_y}{dt^2}+\\Big(\\frac{qB}{m}\\Big)^2v_y=0\\\\\n",
    "\\frac{dv_z}{dt}=0$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "So the solution is of the type $$v_x=A_x cos(\\omega t+\\phi)\\\\ v_y=A_y sin(\\omega t+\\phi)$$ with $$\\omega=\\frac{qB}{m}$$ $\\omega$ is the cyclotron frequency. Since the magnetic field does not perform any work we know that kinetic energy is conserved. The initial energy $\\frac{1}{2}mv_0^2$ is equal to instantaneous kinetic energy $\\frac{1}{2}mv^2$ at any time. So $A_x=A_y=v_0$ and we get $$v_x=v\\ cos(\\omega t+\\phi)\\\\ v_y=v\\ sin(\\omega t+\\phi)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Using the previous slide, it is easy to show that $$x=\\frac{v}{\\omega} sin(\\omega t+\\Phi)\\\\ y=-\\frac{v}{\\omega} cos(\\omega t+\\Phi).$$ We have that for any time t, $x^2+y^2=\\big(\\frac{vm}{qB}\\big)^2$. And the trajectory of the particle is simply a circle with radius $$r_{Larmor}=\\frac{vm}{qB}\\tag{2.8}$$  $r_{Larmor}$ is called the Larmor radius. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "What is the Larmor radius for an electron with initial velocity 1 km/s inside a constant magnetic field of 1T?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.6250000000000016e-09 m\n"
     ]
    }
   ],
   "source": [
    "r_L=1e3*9e-31/(1.6e-19*1)\n",
    "print(r_L,\"m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### The integration of the ODE using Python\n",
    "Now let's integrate our ODE numerically"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "m=9e-31\n",
    "q=-1.6e-19\n",
    "def ODE_integration_B(initial_position,initial_velocity,time_frame,n_steps):\n",
    "    loc=np.zeros((3,n_steps)) #3 for x,y,z  \n",
    "    loc[:,0]=initial_position\n",
    "    v_old=initial_velocity\n",
    "    dt=(time_frame[1]-time_frame[0])/n_steps\n",
    "    B=[0,0,1]\n",
    "    f=np.zeros(3)\n",
    "    v_new=np.zeros(3)\n",
    "    for i in range(1,n_steps,1):\n",
    "        f=q*np.cross(v_old,B)\n",
    "        v_new=f/m*dt+v_old #new momentum\n",
    "        loc[:,i]=v_new*dt+loc[:,i-1] #new position\n",
    "        v_old=v_new\n",
    "    return loc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's try our code now!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_initial=np.array([0,0,0])\n",
    "v_initial=np.array([1000,0,0])\n",
    "time_frame=[0,1e-9]\n",
    "r=ODE_integration_B(r_initial,v_initial,time_frame,2000)\n",
    "plot_2D(r[0,:],r[1,:],1,3,\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The autoscale default from matplotlib does not always work and this is a good example. The distances, like the orbit of an electron inside a field of 1 T, are too small. We need to write an even better plotting function than `plot_2D`. This function is called\n",
    "```python \n",
    "def plot_2D_autoscale(x,y,n_interpolated=1,plot_size=3,plot_axes=\"none\"):\n",
    "```\n",
    "Note that this function has three optional arguments. `n_interpolated` corresponds to the number of interpolation points between time steps, as in `plot_2D`. It's default value is set to `1`, i.e. no interpolation. `plot_size` sets the plot size to `3` by default. Finally, `plot_axes` is set to `\"none\"`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "def plot_2D_autoscale(x,y,n_interpolated=1,plot_size=3,plot_axes=\"none\"):\n",
    "    n = len(x)\n",
    "    k = n_interpolated\n",
    "    #interpolation\n",
    "    x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, x)\n",
    "    y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, y)\n",
    "    #generate figure and axes\n",
    "    fig, ax = plt.subplots(1, 1, figsize=(plot_size, plot_size))\n",
    "    ax.scatter(x_interpolated, y_interpolated, c=range(n*k), linewidths=0,\n",
    "               marker='o', s=2*plot_size, cmap=plt.cm.jet,) #s is the size of the plotted symbol 'o'\n",
    "    ax.axis('equal')\n",
    "    #compute autoscale parameters\n",
    "    xc=(x.max()+x.min())/2.\n",
    "    x_low=xc-(x.max()-x.min())/2.*1.1\n",
    "    x_high=xc+(x.max()-x.min())/2.*1.1\n",
    "    yc=(y.max()+y.min())/2.\n",
    "    y_low=yc-(y.max()-y.min())/2.*1.1\n",
    "    y_high=yc+(y.max()-y.min())/2.*1.1\n",
    "    #set autoscale parameters\n",
    "    ax.set_xlim(x_low,x_high)\n",
    "    ax.set_ylim(y_low,y_high)\n",
    "    if (plot_axes!=\"axes\"):#so we can switch the axis on or off\n",
    "        ax.set_axis_off()\n",
    "    else:\n",
    "        ax.set_xlabel(\"x (m)\")\n",
    "        ax.set_ylabel(\"y (m)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 300x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_2D_autoscale(r[0,:],r[1,:],plot_axes=\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Clearly, this is not a circle. Using the same strategy to solve this ODE did not work well here, as we are trying to approximate a second order ODE using a first order approach... Before, the underlying structure of motion was close to a straight line (hence first order). Now we have circular motion, which is second order, and cannot be approximated by a straight line. Here again we need to develop a model that preserves the underlying nature of motion. Doing a second order integration scheme is possible with python. \n",
    "\n",
    "However, rather than using this method we are going to use something quite exotic called exponential integrators...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "First, we have to notice that $$\\vec F=q\\vec v\\times \\vec B$$ can be rewritten as $$\\frac{d\\vec p}{dt}=\\frac{q}{m}\\vec p\\times \\vec B.$$ While this is not mathematically correct, we can see intuitively that $$\\frac{d p}{dt}-\\frac{q}{m}B p=0\\tag{2.9}$$\n",
    "This is a first order ordinary differential equation which has $$p=p_0e^{\\frac{qB}{m}t}\\tag{2.10}$$ as a solution. And so we think of using exponential integration. The physical model and the mathematical procedure to solve this equation is explained below. If you feel weary about the method, just glance over it. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "According to the special law of relativity $$\\frac{d\\vec p^\\mu}{dt}=\\frac{q}{m\\gamma}F_{\\mu\\nu}\\vec p^\\nu\\tag{2.11}$$ where $F_{\\mu\\nu}$ is the contravariant electromagnetic field tensor given by \n",
    "$$F_{\\mu\\nu}=\n",
    "\\begin{bmatrix}\n",
    "0&E_x/c&E_y/c&E_z/c \\\\\n",
    "-E_x/c&0&-B_z&B_y \\\\\n",
    "-E_y/c&B_z&0&-B_x \\\\\n",
    "-E_z/c&-B_y&B_x&0\n",
    "\\end{bmatrix}$$\n",
    "and the contravariant four-momentum is \n",
    "$$\\vec p^\\nu=\n",
    "\\gamma m\n",
    "\\begin{bmatrix}\n",
    "c&v_x&v_y&v_z\n",
    "\\end{bmatrix}.$$\n",
    "$\\gamma$ is the Lorentz factor which depends on the particle velocity as $$\\gamma=\\frac{1}{\\sqrt{1-\\frac{v^2}{c^2}}}$$ Eqs. $(2.7)$ and $(2.11)$ are equivalent when the particle velocity is small compare to the speed of light $c$.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now, Eqs. $(2.9)$ and $(2.11)$ are really similar but for the fact that vectors have been omitted in Eq. $(2.9)$. It happens that the definition of the exponential function $$\\exp(x) = \\sum_{k = 0}^{\\infty} {x^k \\over k!} = 1 + {x \\over 1!} + {x^2 \\over 2!} + {x^3 \\over 3!} + {x^4 \\over 4!} + \\cdots$$ can be extended to square matrices (since they multiply) as follow $$\\exp(A) = \\sum_{k = 0}^{\\infty} {A^k \\over k!} = 1 + {A\\over 1!} + {A^2 \\over 2!} + {A^3 \\over 3!} + {A^4 \\over 4!}.$$\n",
    "We can show that the change in momentum with time simply follows from Eq. $(2.10)$ as $$\\vec p ^\\mu(t)=\\exp\\Big(\\frac{q}{m\\gamma}F_{\\mu\\nu}t\\Big)\\vec p ^\\mu(0)$$ providing that $F_{\\mu\\nu}$ is constant in space and time. Note that  $M=\\exp\\Big(\\frac{q}{m\\gamma}F_{\\mu\\nu}t\\Big)$ is a matrix!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "once we have computed the momentum, it can be integrated to obtain the trajectory. We can use a first order integration scheme to achieve this task\n",
    "$$\\vec r_{t+\\Delta t}=\\vec v_{t+\\Delta t}\\Delta t+\\vec r_t$$\n",
    "However, we should use the fact that the solution is an exponential that can be integrated easily\n",
    "$$\\vec r_{t+\\Delta t}^\\mu=\\int_{t}^{t+\\Delta t}\\frac{1}{m\\gamma}\\exp(\\frac{q}{m\\gamma}F_{\\mu\\nu}s)ds\\,\\vec p^\\mu_t+\\vec r^\\mu_t$$\n",
    "While we can integrate this equation using linear algebra theory, we will integrate it numerically using the trapezoid rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We define `Lorentz_factor(v)` that computes the Lorentz factor as a function of a velocity $\\vec v=(v_x,v_y,v_z)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def Lorentz_factor(v):\n",
    "    v2=norm(v)**2\n",
    "    c=299792458\n",
    "    return 1./sqrt(1-v2/c**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now let's define two functions that describe the electric and magnetic field as a function of space and time. Beware that we will redefine these functions later in the notebook. So if you come back to this section these ones will be overwritten."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def get_E(r,t):\n",
    "    return np.array([0,0,0])\n",
    "def get_B(r,t):\n",
    "    return np.array([0,0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "For now, these functions hold constant fields. We will redefine them later with fields that are more complex."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's add another function that computes the electromagnetic field tensor $F_{\\mu\\nu}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def EM_field_tensor(E,B):\n",
    "    c=299792458\n",
    "    F_mu_nu=np.array([0,E[0]/c,E[1]/c,E[2]/c,E[0]/c,0,-B[2],B[1],E[1]/c,B[2],0,-B[0],E[2]/c,-B[1],B[0],0])\n",
    "    F_mu_nu.shape=(4,4)\n",
    "    return F_mu_nu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Let's now add two new functions and a library to measure the computational time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from scipy.linalg import expm\n",
    "from numpy.linalg import norm \n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Let's set the initial conditions to study the trajectory of the electron inside a constant magnetic field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "m=9e-31\n",
    "q=-1.6e-19\n",
    "c=299792458"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It is now time to write our ODE integration using exponential integrators where we use the trapezoid rule to compute the trajectory from the momentum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def ODE_integration_exponential_integrator(initial_position,initial_velocity,time_frame,n_steps,n_integrate):\n",
    "    start_time = time.time()\n",
    "    loc=np.zeros((3,n_steps)) #3 for x,y,z  \n",
    "    loc[:,0]=initial_position\n",
    "    v=initial_velocity\n",
    "    gamma=Lorentz_factor(v)\n",
    "    p_old=np.array([m*c,m*v[0],m*v[1],m*v[2]])*gamma\n",
    "    p_new=np.zeros(4)\n",
    "    t=0\n",
    "    dt=(time_frame[1]-time_frame[0])/n_steps\n",
    "    ds=dt/n_integrate\n",
    "    for i in range(1,n_steps,1): #solution of the momentum equation\n",
    "        B=get_B(loc[:,i-1],t)\n",
    "        E=get_E(loc[:,i-1],t)\n",
    "        F_mu_nu=EM_field_tensor(E,B)\n",
    "        p_new=np.matmul(expm(q/(m*gamma)*F_mu_nu*dt),p_old) \n",
    "        gamma=p_new[0]/(m*c)\n",
    "        P=np.zeros((4,4))\n",
    "        s=0.\n",
    "        dPds=np.eye(4)*ds/2\n",
    "        x=np.zeros(4)\n",
    "        for j in range(0,n_integrate,1): #trapezoidal integration to get the trajectory\n",
    "            s+=ds\n",
    "            if (i>0):\n",
    "                P+=dPds\n",
    "            dPds=expm(q/(m*gamma)*F_mu_nu*s)*ds/2\n",
    "            if (i==0):\n",
    "                P+=dPds\n",
    "            P+=dPds\n",
    "        x=np.matmul(P,p_old)/(m*gamma)\n",
    "        loc[:,i]=x[1:4]+loc[:,i-1] #new position\n",
    "        p_old=p_new\n",
    "        t+=dt\n",
    "    #print(\"--- %s seconds ---\" % (time.time() - start_time))\n",
    "    return loc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Can we make the function simpler? Let's compute the trajectory from the momentum using a simple first order integration scheme."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def ODE_integration_first_order_exponential_integrator(initial_position,initial_velocity,time_frame,n_steps):\n",
    "    start_time = time.time()\n",
    "    loc=np.zeros((3,n_steps)) #3 for x,y,z  \n",
    "    loc[:,0]=initial_position\n",
    "    v_old=initial_velocity\n",
    "    p_old=np.zeros(4)\n",
    "    p_old[0]=m*c\n",
    "    p_old[1:4]=m*v_old\n",
    "    p_old*=Lorentz_factor(initial_velocity)\n",
    "    p_new=np.zeros(4)\n",
    "    dt=(time_frame[1]-time_frame[0])/n_steps\n",
    "    f=np.zeros(3)\n",
    "    v_new=np.zeros(3)\n",
    "    gamma=Lorentz_factor(v_old)\n",
    "    t=0\n",
    "    for i in range(1,n_steps,1):\n",
    "        B=get_B(loc[:,i-1],t)\n",
    "        E=get_E(loc[:,i-1],t)\n",
    "        F_mu_nu=EM_field_tensor(E,B)\n",
    "        p_new=np.matmul(expm(q/(m*gamma)*F_mu_nu*dt),p_old)\n",
    "        gamma=p_new[0]/(m*c)\n",
    "        v_new=p_new[1:4]/(m*gamma)\n",
    "        loc[:,i]=v_new*dt+loc[:,i-1] #new position\n",
    "        p_old=p_new\n",
    "        t+=dt\n",
    "    #print(\"--- %s seconds ---\" % (time.time() - start_time))\n",
    "    return loc\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now let's run both functions and compare their results to the analytical solution of the Larmor radius given by Eq. $(2.8)$. We start with the one where the trapezoid rul i used to compute the trajectory from the momentum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gyration time = 3.534291735288518e-11 s\n",
      "Larmor radius = 5.6250000000000016e-09 m\n",
      "-5.623743503265955e-09 5.623743503263875e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_initial=np.array([0,0,0])\n",
    "v_initial=np.array([1000,0,0])\n",
    "t_gyration=m/(abs(q)*norm(get_B(r_initial,0)))*(2*math.pi)\n",
    "time_frame=[0,t_gyration]\n",
    "print('Gyration time =',t_gyration,'s')\n",
    "print('Larmor radius =',norm(v_initial)*m/(abs(q)*norm(get_B(r_initial,time_frame[0]))),'m')\n",
    "r=ODE_integration_exponential_integrator(r_initial,v_initial,time_frame,150,6)\n",
    "print(r[0,:].min(),r[0,:].max())\n",
    "plot_2D_autoscale(r[0,:],r[1,:],n_interpolated=1,plot_size=5,plot_axes=\"axes\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "This is a nice circle. And look at the value of the Larmor radius as computed analytically and and the one computed by the function. It's very accurate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now let's look at the other function. The one using the first order time integration for the trajectory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor radius = 5.6250000000000016e-09 m\n",
      "-5.743220979103797e-09 5.5076015300845365e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r=ODE_integration_first_order_exponential_integrator(r_initial,v_initial,time_frame,150)\n",
    "print('Larmor radius =',norm(v_initial)*m/(abs(q)*norm(get_B(r_initial,time_frame[0]))),'m')\n",
    "print(r[0,:].min(),r[0,:].max())\n",
    "plot_2D_autoscale(r[0,:],r[1,:],n_interpolated=1,plot_size=5,plot_axes=\"axes\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "All is good. The output looks like a circle. But pay attention to the value of the Larmor radius, as computed by the function and compare it to the analytical value. They are slightly different. Is this a problem?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    " Let's find out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor radius = 5.6250000000000016e-09 m\n",
      "-2.9804726080783246e-08 4.122206137687116e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time_frame=[0,109*t_gyration]\n",
    "r=ODE_integration_first_order_exponential_integrator(r_initial,v_initial,time_frame,150)\n",
    "print('Larmor radius =',norm(v_initial)*m/(abs(q)*norm(get_B(r_initial,time_frame[0]))),'m')\n",
    "print(r[0,:].min(),r[0,:].max())\n",
    "plot_2D_autoscale(r[0,:],r[1,:],n_interpolated=1,plot_size=5,plot_axes=\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The Larmor radius is completely off. The color are all jumbled up but this is due to aliasing! It is normal. Nothing to worry about."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "How about the trapezoid integration?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Larmor radius = 5.6250000000000016e-09 m\n",
      "-5.3497331788990875e-09 5.349733178685756e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r=ODE_integration_exponential_integrator(r_initial,v_initial,time_frame,150,6)\n",
    "print('Larmor radius =',norm(v_initial)*m/(abs(q)*norm(get_B(r_initial,time_frame[0]))),'m')\n",
    "print(r[0,:].min(),r[0,:].max())\n",
    "plot_2D_autoscale(r[0,:],r[1,:],n_interpolated=1,plot_size=5,plot_axes=\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Much better. After 109 gyration, we have roughtly the same error than `ODE_integration_first_order_exponential_integrator` had for one turn! You can check that both functions are actually giving good results, when the time step is small enough. However, you will discover that `ODE_integration_exponential_integrator` does much better for larger time steps, especially if you are increasing `n_integrate`. So, again, beware of time stepping! In fact, for inhomegeneous fields, this is `n_steps` that has to be increased."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Particle trajectories inside homogeneous steady-state electric *and* magnetic fields\n",
    "### The effect of parallel electric fields\n",
    "Now we combine the effect of both electric fields and magnetic fields. If a magnetic field is given by $\\vec B=(B_x,B_y,B_z)$, then the particle will gyrate in the $(x,y)$ plane. But what happens if there is also and electric field along the z-axis? Note that by **parallel electric fields** we mean parallel to $\\vec B$. In this case, we need to solve the following system of differentiual equations.\n",
    "$$\\frac{d^2v_x}{dt^2}=\\frac{q}{m}\\frac{dv_y}{dt}B_z\\\\\n",
    "\\frac{d^2v_y}{dt^2}=-\\frac{q}{m}\\frac{dv_x}{dt}B_z\\\\\n",
    "\\frac{dv_z}{dt}=\\frac{q}{m}E_z$$\n",
    "As before, we have a circular trajectory in the $(x,y)$ plane and a \"free\" fall along the $z$ axis. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Since we expect motion in all three directions, we need to write a new function that plots in three dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def plot_3D_autoscale(loc,n_interpolated=1,plot_size=3,plot_axes=\"none\"):\n",
    "    from mpl_toolkits.mplot3d import Axes3D\n",
    "    n = len(loc[0])\n",
    "    k = n_interpolated\n",
    "    #interpolation\n",
    "    x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[0,:])\n",
    "    y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[1,:])\n",
    "    z_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[2,:])\n",
    "    #generate figure and axes\n",
    "    fig = plt.figure(figsize=(plot_size,plot_size))\n",
    "    ax = fig.add_subplot(111, projection='3d')\n",
    "    ax.scatter(x_interpolated, y_interpolated, z_interpolated, c=range(n*k), linewidths=0,\n",
    "               marker='o', s=2*plot_size, cmap=plt.cm.jet,) #s is the size of the plotted symbol 'o'\n",
    "    #compute autoscale parameters\n",
    "    xc=(loc[0,:].max()+loc[0,:].min())/2.\n",
    "    x_low=xc-(loc[0,:].max()-loc[0,:].min())/2.*1.1-1e-12\n",
    "    x_high=xc+(loc[0,:].max()-loc[0,:].min())/2.*1.1+1e-12\n",
    "    yc=(loc[1,:].max()+loc[1,:].min())/2.\n",
    "    y_low=yc-(loc[1,:].max()-loc[1,:].min())/2.*1.1-1e-12\n",
    "    y_high=yc+(loc[1,:].max()-loc[1,:].min())/2.*1.1+1e-12\n",
    "    zc=(loc[2,:].max()+loc[2,:].min())/2.\n",
    "    z_low=zc-(loc[2,:].max()-loc[2,:].min())/2.*1.1-1e-12\n",
    "    z_high=zc+(loc[2,:].max()-loc[2,:].min())/2.*1.1+1e-12\n",
    "    #set autoscale parameters\n",
    "    ax.set_xlim(min(x_low,y_low,z_low),max(x_high,y_high,z_high))\n",
    "    ax.set_ylim(min(x_low,y_low,z_low),max(x_high,y_high,z_high))\n",
    "    ax.set_zlim(min(x_low,y_low,z_low),max(x_high,y_high,z_high))\n",
    "    if (plot_axes!=\"axes\"):#so we can switch the axis on or off\n",
    "        ax.set_axis_off()\n",
    "    else:\n",
    "        ax.set_xlabel(\"x (m)\")\n",
    "        ax.set_ylabel(\"y (m)\")\n",
    "        ax.set_zlabel(\"z (m)\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_E(r,t):\n",
    "    return np.array([0,300,10])\n",
    "def get_B(r,t):\n",
    "    return np.array([0,0,-1])\n",
    "r_initial=np.array([0,0,0])\n",
    "v_initial=np.array([1000,0,0])\n",
    "t_gyration=m/(abs(q)*norm(get_B(r_initial,time_frame[0])))*(2*math.pi)\n",
    "time_frame=[0,3*t_gyration]\n",
    "r=ODE_integration_exponential_integrator(r_initial,v_initial,time_frame,150,6)\n",
    "plot_3D_autoscale(r,n_interpolated=10,plot_size=8,plot_axes=\"axes\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We need to install a 3D plotting library now. It is called [plotly](https://plot.ly/python/3d-scatter-plots/). Open the terminal window from Anaconda Navigator and type `conda install -c conda-forge plotly`. It is also good for interactive 2D plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def plotly_3D(loc,n_interpolated=1,sphere_size=1,opacity_value=0,scale_axis='x',autoscale=False):\n",
    "    import plotly.offline as py\n",
    "    import plotly.graph_objs as go\n",
    "    py.init_notebook_mode()\n",
    "    n = len(loc[0])\n",
    "    k = n_interpolated\n",
    "    #interpolation\n",
    "    x_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[0,:])\n",
    "    y_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[1,:])\n",
    "    z_interpolated = np.interp(np.arange(n * k), np.arange(n) * k, loc[2,:])\n",
    "    trace = go.Scatter3d(\n",
    "        x = x_interpolated,\n",
    "        y = y_interpolated,\n",
    "        z = z_interpolated,\n",
    "        mode='markers',\n",
    "        name = 'test',\n",
    "        marker=dict(\n",
    "            size=sphere_size,\n",
    "            color=np.linspace(0, 1, len(r[0,:])*k), # set color to an array/list of desired values\n",
    "            colorscale='Jet',   # choose a colorscale\n",
    "            opacity=opacity_value\n",
    "        )\n",
    "    )\n",
    "    xc=(loc[0,:].max()+loc[0,:].min())/2.\n",
    "    x_low=xc-(loc[0,:].max()-loc[0,:].min())/2.*1.1-1e-12\n",
    "    x_high=xc+(loc[0,:].max()-loc[0,:].min())/2.*1.1+1e-12\n",
    "    yc=(loc[1,:].max()+loc[1,:].min())/2.\n",
    "    y_low=yc-(loc[1,:].max()-loc[1,:].min())/2.*1.1-1e-12\n",
    "    y_high=yc+(loc[1,:].max()-loc[1,:].min())/2.*1.1+1e-12\n",
    "    zc=(loc[2,:].max()+loc[2,:].min())/2.\n",
    "    z_low=zc-(loc[2,:].max()-loc[2,:].min())/2.*1.1-1e-12\n",
    "    z_high=zc+(loc[2,:].max()-loc[2,:].min())/2.*1.1+1e-12\n",
    "    ratio_x=1\n",
    "    ratio_y=1\n",
    "    ratio_z=1\n",
    "    if (autoscale==False):\n",
    "        max_length=max(abs(x_high-x_low),abs(y_high-y_low),abs(z_high-z_low))\n",
    "        ratio_x=abs(x_high-x_low)/max_length\n",
    "        ratio_y=abs(y_high-y_low)/max_length\n",
    "        ratio_z=abs(z_high-z_low)/max_length\n",
    "        max_ratio=max(ratio_x,ratio_y,ratio_z)\n",
    "        ratio_x/=max_ratio\n",
    "        ratio_y/=max_ratio\n",
    "        ratio_z/=max_ratio\n",
    "\n",
    "    data = [trace]\n",
    "    layout = go.Layout(\n",
    "        autosize=False,\n",
    "        margin=dict(\n",
    "            l=0,\n",
    "            r=0,\n",
    "            b=0,\n",
    "            t=0\n",
    "        ),\n",
    "        paper_bgcolor = 'grey',\n",
    "        scene = dict(\n",
    "            aspectratio = dict( x=ratio_x, y=ratio_y, z=ratio_z),\n",
    "            xaxis = dict(\n",
    "                gridcolor='rgb(255, 255, 255)',\n",
    "                zerolinecolor='rgb(255, 255, 255)',\n",
    "                showbackground=False,\n",
    "                backgroundcolor='rgb(230, 230,230)',\n",
    "                nticks=4, range = [x_low,x_high],),\n",
    "            yaxis = dict(\n",
    "                gridcolor='rgb(255, 255, 255)',\n",
    "                zerolinecolor='rgb(255, 255, 255)',\n",
    "                showbackground=False,\n",
    "                backgroundcolor='rgb(230, 230,230)',\n",
    "                nticks=4, range = [y_low,y_high],),\n",
    "            zaxis = dict(\n",
    "                gridcolor='rgb(255, 255, 255)',\n",
    "                zerolinecolor='rgb(255, 255, 255)',\n",
    "                showbackground=False,\n",
    "                backgroundcolor='rgb(230, 230,230)',\n",
    "                nticks=4, range = [z_low,z_high],),),\n",
    "        height =300,\n",
    "        width=500,\n",
    "        hovermode=False\n",
    "        )\n",
    "    fig = go.Figure(data=data, layout=layout)\n",
    "    py.iplot(fig, filename='3d-scatter-colorscale')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
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   "outputs": [],
   "source": [
    "#plotly_3D(r,n_interpolated=10,sphere_size=2,autoscale=False)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "### EXB drifts\n",
    "Let's suppose that we align the coordinate system along $\\vec{B}$ so that $\\vec{B}=B\\hat z$ and $\\vec E=E\\vec x$, we have\n",
    "$$\\frac{dv_x}{dt}=\\frac{q}{m}(E+v_yB)\\\\\n",
    "\\frac{dv_y}{dt}=-\\frac{q}{m}v_xB\\\\\n",
    "\\frac{dv_z}{dt}=0$$\n",
    "If we have no initial velocity along the z-axis, then the trajectory is fully contained n the $(x,y)$ plane. Taking the derivative with respect to time and combining equations we find that\n",
    "$$\\frac{d^2v_x}{dt^2}+\\Big(\\frac{qB}{m}\\Big)^2v_x=0\\\\\n",
    "\\frac{d^2v_y}{dt^2}+\\Big(\\frac{qB}{m}\\Big)^2v_y=-\\Big(\\frac{q}{m}\\Big)^2BE$$\n",
    "which solution is \n",
    "$$v_x=v\\ cos(\\omega t+\\phi)\\\\ v_y=v\\ sin(\\omega t+\\phi)-\\frac{E}{B}$$\n",
    "We have supposed that B and E are perpendicular here. To get the general expression of the drift we just have to take the component of $\\vec E$ that is perpandicular to $\\vec B$ or\n",
    "$$\\vec v_{E\\times B}=\\frac{\\vec E\\times \\vec B}{B}$$\n",
    "Note that both positive and negative particles drift in the same direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
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   "source": [
    "def get_E(r,t):\n",
    "    return np.array([0,10,0])\n",
    "def get_B(r,t):\n",
    "    return np.array([0,0,1])\n",
    "r_initial=np.array([0,0,0])\n",
    "v_initial=np.array([10,0,0])\n",
    "t_gyration=m/(abs(q)*norm(get_B(r_initial,time_frame[0])))*(2*math.pi)\n",
    "time_frame=[0,11*t_gyration]\n",
    "r=ODE_integration_exponential_integrator(r_initial,v_initial,time_frame,250,8)\n",
    "#plotly_3D(r,n_interpolated=20,sphere_size=2,autoscale=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Guiding center\n",
    "When no physical processes take place on the cyclotron time scale, it is possible to simplify the trajectory by focusing only on the motion of the guiding center of the particle. The position of the guiding center is given by $$ \\vec r_p=\\frac{1}{t_{cyclotron}}\\int_0^{t_{cyclotron}}\\vec r_p(t)dt$$\n",
    "In this case, the particle motion is by adding all the velocities together:\n",
    "1. Drifts relative to $\\vec E$\n",
    "$$\\vec v_E = \\left( 1 + \\frac{1}{4}r_{Larmor}^2\\nabla^2 \\right) \\frac{\\vec E\\times\\vec B}{B^2}\\tag{2.12}$$\n",
    "2. Drifts relative to $\\vec B$\n",
    "$$\\vec v_B =\\frac{2eT}{qB}\\frac{\\vec{R}_c\\times\\vec{B}}{R_c^2 B}\\tag{2.13}$$\n",
    "\n",
    "In Eq. $(2.13)$ the temperature $T$ is in $V$ and $e$ is the elementary charge. The term $eT$ is in joules. It correspond to the microscopic energy carried by particles in a Maxwellian distribution. Note that to convert $volt$ to $kelvin$ one can use the fact that $k_BT(K)=eT(V)$. Eq. $(2.13)$ also has the radius of curvature $\\vec R_c$ of the particle. \n",
    "\n",
    "This representation is relatively limited in scope. It breaks down when large gradients or fast time variations occur as the particle moves along its trajectory.  However, computations based on Eqs. $(2.12)$ and $(2.13)$ are faster than using Eq. $(2.11)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problems\n",
    "\n",
    "### Problem 1\n",
    "Compare the final positions of the particle as computed by the numerical integration of the ordinary differential equation using `ODE_integration_E` and compare it to the analytical (i.e. correct) integration given by Eq. $(2.5)$. To do this, plot the final distance obtained by `ODE_integration_E` along the y-axis as a function of the time step and show that it converges towards the value of the analytical solution \n",
    "\n",
    "### Problem 2\n",
    "Compute the angle of deflection of an electron \"flying by\" a fixed ion as a function of the initial velocity of the electron. Infer the dependence of the angle of deflection with velocity. Comment on how the discretization impacts the angle at low velocities. \n",
    "\n",
    "### Problem 3\n",
    "Plot the strength (color) and direction (arrows) of the electric field produced by one single charge in 2D. Try to do it in 3D after that. While it is not that difficult, 3D plot tend to be difficult to read if not done properly. \n",
    "\n",
    "### Problem 4\n",
    "1. Write a piece of code to compare the deviation between `ODE_integration_exponential_integrator` and the actual Larmor radius. We call the difference between them the error $e$.\n",
    "2. Vary the number of time steps and the number of integration steps and plot how the error $e$ varies as a function of both.\n",
    "3. What can you conclude?\n",
    "\n",
    "### Problem 5\n",
    "When electric fields and magnetic fields are presents, charged particles do not simply gyrate, they move along the electric field direction also. When the electric field is purely perpendicular to B, the charge particle is said to drift, hence the name *ExB drift*. We are going to use `ODE_integration_exponential_integrator` to compute the drift velocity of an electron inside a magnetic field $\\vec B=(0,0,1)$ and in an electric field $\\vec E=(100,0,0)$.\n",
    "1. Compute analytically the gyration period $t_{Larmor}$\n",
    "2. What is its numerical value?\n",
    "3. Starting with $t_{initial}=0$ and ending at $t_{final}=5\\,t_{Larmor}$, find the distance traveled by the electron and infer the velocity from this value.\n",
    "4. Redo 1,2 and 3 for a proton. Is the proton traveling in the same direction?\n",
    "\n",
    "### Problem 6\n",
    "If you remember we had a little problem with `OED_integration_E`. If we integrated our ODE for too long, then an electron inside a 1V electric field would eventually go faster than the speed of light. `ODE_integration_exponential_integrator` takes into account relativistic correction and really avoid this problem.\n",
    "1. Using the exact same initial values of position and velocity, find out what is the velocity of the electron after 3s. If it does go faster than the speed of light, increase the number of time steps.\n",
    "\n",
    "Let's imagine that you want to build a particle accelerator using a steady electric field of $1kV/m$ to accelerate an electron to $0.999c_{light}$\n",
    "2. How long should the accelerator be?\n",
    "2. How long should it be if you ignore relativistic corrections, i.e. use `OED_integration_E`?"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Â© Pierre Gourdain, The University of Rochester, 2020"
   ]
  }
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